I am not too familiar with the pill she is taking, but if she has been consistent since the throwing up incident then there is a very small chance of her being/becoming pregnant. Also, vomiting 3.5 hours after taking the pill should be enough time for her body to digest it.

I'm on Alesse and have had a couple of missed pill incidents, but because of the nature of the pills, I was still fully under the effect of the birth control.